From the upper bound perspective, the first branch matches dynamic fusion trees [1]}, the second branch is based on an extension of the techniques from Beame and Fich [2]}, and the last branch is based on an extension of dynamic van Emde Boas trees [3]}. Note that the lower bound implies that we cannot support operations in constant time for general \(n\)  and \(w\) . Hence, a natural question is if practical models of computation capturing modern hardware can allow us to overcome the superconstant lower bound.
